Reliable Stabilization of Interconnected Systems Using a Switching Multilayer Control Structure

Abstract

The dynamic systems consisting of a number of interconnected subsystems, such as power systems, ecological systems, transportation systems, and etc., widespreadly appear in the natural world and man’s life. One of the most striking characteristic of such a system is its interconnection structure, which may change while the system is operating, because of breakdown of circuits, or sudden change of loads, etc. Hence in the design of interconnected control systems, besides assuring the system to have satisfactory performance under the normal interconnection, the effects on the system, of interconnection perturbations, which may occur should also be considered, particularly for strongly interconnected systems. Siljak first recognized this point. In 1972, he presented the notion of connective stability for large-scale interconnected dynamic systems from an analytic point of view, and gave the sufficient conditions for an interconnected system to possess the connective exponential stability by using the method or vector Lyapunov functions. In 1976, from a design point of view, Siljak dealt with the problem of determining the conditions satisfied by perturbations of interconnection structure under which the perturbations do not violate the stability of the closed-loop system. In [3], Geromel, et al. considered the problem of stability of large-scale interconnected systems with a two-level control subjected to structural perturbations between two levels by means of Lyapunov vecro functions. In a word, all these papers have concentrated on structural perturbations which may occur in interconnected control systems.